24th ICDERS July 28 – August 2, 2013 Taipei, Taiwan

Macroscopic Structure of Fast Deflagrations and Detonationsin Hydrogen-Air Mixtures with Concentration Gradients

L. R. Boeck, F. M. Berger, J. Hasslberger, F. Ettner and T. SattelmayerLehrstuhl fur Thermodynamik, Technische Universitat Munchen

Garching, Germany

1 Introduction

Research on explosion hazards in nuclear power plants has shown that hydrogen-air mixtures with con-centration gradients constitute realistic accident scenarios [1]. Distribution of hydrogen released intolarge rooms is dominated by the buoyancy effect rather than by diffusion. Only comparably long timesallow for formation of homogeneous mixtures via molecular diffusion. Little is known about the influ-ence of concentration gradients on flame acceleration and the onset of detonation for gradients beingoriented perpendicularly to the main direction of flame propagation. Previous studies mainly focusedon flame front and shock tracking via photodiodes and pressure transducers [2–4], as well as on 2Dnumerical simulation of the entire process [5–8]. However, all this experimental and numerical data israrely validated by means of optical measurement techniques. Ishii et al. [9] analyzed detonation propa-gation in hydrogen-air mixtures with vertical concentration gradients and gave an insight into detonationstructure. Lieberman and Shepherd [10] optically examined detonation propagation through mixturesforming a spatial concentration gradient with a diluent. Both studies concluded influences on propa-gation velocity and detonation front curvature. The present work thus aims at giving further details ondeflagration and detonation propagation in inhomogeneous hydrogen-air mixtures.

2 Experimental Setup

Deflagration and detonation phenomena are studied in a closed rectangular channel with a length of5.4 m and a cross section of 300 mm x 60 mm as described in detail in [3]. The channel comprisestwo sections, one part for promoting flame acceleration via obstacles after spark ignition and an unob-structed second part. The first section is 2.05 m long and enables obstacle application. In this work,the configuration BR60S300 with a blockage ratio (BR) of 60 % and an intermediate spacing (S) of300 mm is investigated. Optical access is achieved via two facing quartz glass windows. Individualpositioning of the window section along the channel axis allows for observation of all relevant phenom-ena. A defined hydrogen concentration gradient in air is generated perpendicular to the main directionof flame propagation. For this purpose, a deflection mechanism at the channel’s top is used to build upa hydrogen layer in the upper part of the channel which stratifies through buoyancy and diffusion as afunction of time. Diffusion times td vary from 3 s up to 60 s and define the steepness of the gradient.

Correspondence to: boeck@td.mw.tum.de 1

Boeck L.R. Fast Flame and Detonation Structures in Inhomogeneous Mixtures

The latter time represents an entirely homogeneous mixture. Further details on the injection mechanismincluding validation measurements and simulations can be found in [3]. All experiments are conductedat an initial pressure of 1 atm and ambient temperature. Optical investigations include color schlieren,shadowgraph and OH* chemiluminescence imaging. Schlieren and shadowgraph images are capturedsimultaneously to OH* chemiluminescence. Images are taken at a maximum frame rate of 72000 fpsand a minimum shutter speed of 370 ns using Photron SA-X, SA5 and image intensified Photron APXI2

high-speed cameras. For illumination, a constant 300 W Xe arc light source is used. It is noteworthythat self-absorption plays a role for OH* chemiluminescence imaging due to the considerable opticaldepth of the channel. Therefore, structures emerging from positions closer to the recording camera mayappear with a higher weighting than structures at a larger distance.

3 Fast Flames in Inhomogeneous Mixtures

Figure 1 shows representative images of shock waves and flames in a homogeneous (left) and inhomoge-neous mixture (right, td = 3 s) for 15 %vol hydrogen in air. Records are taken at the last obstacle passageat a distance of 2.05 m from the point of ignition. Although the channel width of 300 mm is distinctlylarger than in comparable facilities, a low curvature of the observed structures in the spanwise-directionof the channel leads to an adequate image quality.

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100500 150 200 100500 150 200

shock front shock front

Δ

ρ

flame frontflame front

Figure 1: Color schlieren images showing shock waves and flame front in 15 %vol H2-air mixture in theBR60S300 obstacle configuration; Left: homogeneous mixture; Right: inhomogeneous mixture withsteep concentration gradient (td = 3 s).

The formation of shock waves ahead of the turbulent reaction zone is clearly visible. Shock wavesreflected off the obstacle have not yet interacted with the flame front at the stage shown in Figure 1.The particular strength of the leading shock front and the reflected waves can be qualitatively assessedby interpreting the recorded colors (see ∇ρ plot, Figure 1). The maximum deflection of parallel lightexceeds the colored region of the schlieren edge and indicates the highest appearing density gradients.Extensive studies of flame acceleration by means of conventional measurement techniques (photodiodesand pressure transducers) in this facility demonstrate the accelerating effect of concentration gradientsfor this obstacle configuration at average volumetric hydrogen concentrations lower than 22.5 %vol [11].Concentration gradients lead to a reduction of the distance between leading shock and reaction zone atthe examined position with a flame slightly oriented towards the top. Despite the mixture inhomogene-ity, macroscopic flame surfaces remain in the same order of magnitude in the obstructed channel.Figures 2 and 3 show fast deflagrations in the unobstructed part of the channel for two different averagevolumetric hydrogen concentrations. The white rectangles at the top mark the positions of the hydro-gen deflection mechanism. The propagation behavior in the smooth channel is clearly different fromthe obstructed channel. Nearly symmetrical flame fronts and leading shock waves with respect to thechannel axis can be observed in homogeneous mixtures. In contrast, steep concentration gradients causestreched flames with very large macroscopic flame surfaces and curved leading shock waves. The largeflame surface leads to a high integral heat release rate, which is likely to cause the observed acceleratingeffect of concentration gradients in unobstructed channels [11]. As the mixture is most reactive at thechannel top, providing the highest local laminar burning velocity and the highest local expansion ratio,

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Boeck L.R. Fast Flame and Detonation Structures in Inhomogeneous Mixtures

the flame tip is located in this region. An interaction of flame and turbulent boundary layer along theupper wall is believed to additionally support this enlargement of flame surface. Figure 3 shows themost pronounced difference in flame shapes observed in the reported series of measurements. While theflame in the homogeneous mixture is clearly separated from the leading shock, the flame in the inho-mogeneous mixture is almost coupled with the leading shock in the upper region. Subsequent onset ofdetonation seems likely in this mixture. Shock and flame velocities extracted from the optical recordsare presented in Table 1. The inhomogeneous mixture clearly causes higher shock and flame velocitiescompared to the homogeneous mixture.

Table 1: Measured average velocities in the observed area corresponding to Figures 2 and 3.

15 %vol td = 60 s td = 3 s

shock velocity [m/s] 660 700flame velocity [m/s] 350 390

20 %vol td = 60 s td = 3 s

shock velocity [m/s] 810 950flame velocity [m/s] 570 ≈ vshock

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100500 150 200

Δ

ρ

shock frontflame front flame front

100500 150 200

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Figure 2: Color schlieren images showing shock waves and flame front in 15 %vol H2-air mixturepropagating in the unobstructed part of the channel; First row: homogeneous mixture at two differentstages; Second row: inhomogeneous mixture with steep concentration gradient (td = 3 s) at two differentstages.

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100500 150 200

Δ

ρ

shock frontflame front

100500 150 200

shock frontflame front

Figure 3: Color schlieren images showing shock waves and flame front in 20 %vol H2-air mixturepropagating in the unobstructed part of the channel; Left: homogeneous mixture; Right: inhomogeneousmixture with steep concentration gradient (td = 3 s).

24th ICDERS – July 28 – August 2, 2013 – Taiwan 3

Boeck L.R. Fast Flame and Detonation Structures in Inhomogeneous Mixtures

4 Detonations in Inhomogeneous Mixtures

At average hydrogen concentrations higher than 20 %vol, detonations can be observed in the unob-structed section of the channel. Shadowgraph and OH* chemiluminescence images are presented inFigure 4, where 8bit greyscale OH* chemiluminescence records are transferred into color maps for bet-ter visualization of local intensities.

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t = 60s (homogeneous)d t = 10sd t = 7.5sd t = 5sd t = 3sd

255

0

Raw OH* chemiluminescence

Shadowgraph

Processed OH* chemiluminescence

Figure 4: Shadowgraph and OH* chemiluminescence images of detonations in 30 %vol H2-air mixturewith different concentration gradients.

The detonation front for the homogeneous 30 %vol hydrogen-air mixture is captured as a reference. Anearly planar front with a very narrow reaction zone is observed for this case, as can be expected. Themeasured propagation velocity is nearly constant with a deficit of about 2 % compared to the theoreticalChapman-Jouguet velocity. Reaction is evenly distributed along the whole channel height, as can beseen in the OH* chemiluminescence image. With increasing concentration gradients, the detonationfront becomes curved. This has already been observed in general by Ishii et al. [9]. Ettner [7] analyzespossible solutions at the channel walls to achieve wall-parallel flow behind the leading shock in a curveddetonation front. He distinguishes three possible mechanisms:

1. Bending of the leading shock

2. Regular shock reflection

3. Development of a Mach stem

In the presented work, a Mach stem can be observed at the bottom of the channel for steep concentrationgradients corresponding to td = 3 s and 5 s. This observation confirms numerical simulations shownin [7]. At less pronounced concentration gradients (td = 7.5 s and 10 s), it can be seen that local deflectionangles remain comparably small. The Mach stem height is either decreased, direct reflection of theshock front from the bottom wall occurs, or bending of the leading shock leads to wall-parallel flow.OH* chemiluminescence images show a shift of the reaction zone towards the top wall for moderateconcentration gradients. The steepest concentration gradient (td = 3 s) with Mach stem formation leadsto high local luminescence right at the top plate interaction, as well as behind the Mach stem. Detonationpropagation is maintained even though measured propagation velocities decrease with concentrationgradients, as reported in [2]. It cannot be concluded directly from the images whether the reaction zoneis coupled to the leading shock along the whole channel height and width. Nevertheless, an importantfinding is that reaction in the lean region at the channel bottom is maintained due to the high temperature

24th ICDERS – July 28 – August 2, 2013 – Taiwan 4

Boeck L.R. Fast Flame and Detonation Structures in Inhomogeneous Mixtures

ratio produced by the Mach stem. This effect can be reproduced by calculating the thermodynamicconditions behind the Mach stem and the vertical part of the leading shock at the channel top. As arguedin [7], the shape of the observed curved detonation structure remains unchanged during propagation ifinstability effects are neglected. Following this simplified approach and taking into account the localmixture properties along the channel height at a diffusion time of td = 3 s and 30 %vol average hydrogenconcentration (Table 2), it is obvious that the local shock Mach number is higher at the channel bottomthan at the top. This in turn results in a higher temperature ratio at the Mach stem. Induction timesare calculated for the particular local mixture compositions with an exemplary detonation velocity of2000 m/s. It can be shown that self-ignition is promoted behind the Mach stem in the leanest region ofthe channel. This is due to the more pronounced sensitivity of induction time on temperature than onhydrogen concentration. Additional calculations of corresponding induction lengths reveal a noticeablefact. At the channel bottom, the calculated length predicts close coupling of shock wave and reactionzone. At the top however, pronounced and easily visible decoupling should be expected. As this isnot the case in the presented shadowgraph images, additional underlying mechanisms, which cannot becaptured by simplified one-dimensional approaches, may be responsible for self-sustaining detonationpropagation in mixtures with concentration gradients. This aspect requires further investigations.

Table 2: Parameters of detonation in the inhomogeneous mixture. Calculations are based on Cantera[12], combined with the Shock and Detonation Toolbox [13] employing a detailed reaction mechanismby O’Conaire et al. [14].

Location H2 conc. Shock Ma Post-shock temp. Induction time Induction length[%vol] [-] [K] [s ·10−6] [m ·10−3]

Channel top 52.4 4.1 1225 17 34Channel bottom 9.5 5.5 1853 0.19 0.38

Another striking aspect, which is shown in the shadowgraph images, is the stretched indistinct grey arearight behind the leading shock front for steep concentration gradients. The area width increases withdecreasing diffusion time. This effect might either originate from viewing a curved detonation frontin the channel with an optical depth of 300 mm, or from local decoupling of reaction zone and shockwave due to instability of the detonation front induced by concentration gradients. Turbulent burning ofinitially unburnt fractions of the mixture at a certain distance from the leading shock would consequentlylead to an appearance of the detonation front as it is observed.

5 Conclusions and Outlook

Influences of concentration gradients on the macroscopic shape of fast deflagrations and detonations areoptically investigated in this study. For deflagrations in the unobstructed channel, significantly largermacroscopic flame surfaces can be observed. Higher propagation velocities of flame and leading shockfront are measured, which is most likely due to the growth of flame surface and the related increaseof the integral heat release rate. The detonation study unveils curved detonation fronts resulting fromconcentration gradients. Steep gradients lead to the formation of a Mach stem at the bottom wall.Reaction in the leanest part of the mixture is maintained by the high temperature ratio produced by theMach stem.

Future optical investigations should reveal further information on flame structure and details of thedetonation front, especially on the dynamics and mechanisms of detonation propagation in mixtureswith concentration gradients. Additionally, detonation characteristics will be studied with soot foilrecords.

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Boeck L.R. Fast Flame and Detonation Structures in Inhomogeneous Mixtures

The presented work is funded by the German Federal Ministry of Economics and Technology (BMWi) onthe basis of a decision by the German Bundestag (project no. 1501425 and 1501338 ) which is gratefullyacknowledged.

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[4] Vollmer KG, Ettner F and Sattelmayer T. (2011). Influence of Concentration Gradients on FlameAcceleration in Tubes. Sci. Technol. Energ. Mater. 72: 74.

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